What is the goal of the analysis? If it was to determine the springback of the sheet after the die retracts, you have that. The rigid body motion after contact is lost can be subtracted off the deformation result.

You could add a small pressure load to the top surface of the sheet. Leave that pressure load on until the punch retracts, then ramp the pressure to zero in the next load step. Then gravity may be able to hold the part against the die.

You could try Transient Structural, but depending on the speed of the punch, the part may to want to launch itself toward the punch due to the springback. You will then have to let it fall back under a Gravity load until it settles in the die, but it might not be sitting level at the end time.